In the conventional art, as methods for numerical analysis for flow velocity distribution, stress distribution, heat distribution, and the like by numerical analysis, known techniques include a finite element method, a finite volume method, a voxel method, and a particle method.
In general, such a method for numerical analysis is constructed from pre process, solver process, and post process. Then, the pre process generates a calculation data model. Then, the solver process calculates the above-mentioned physical values by using the calculation data model and a governing equation having been discretized (referred to as a discretized governing equation, hereinafter).
In a conventional finite volume method, for example, the analysis domain is divided into a plurality of domains. Then, physical values in each divided domain are calculated by using the volume of each divided domain, the area of the boundary surface between adjacent divided domains, and the normal vector of the boundary surface.
In a finite volume method, the pre process generates a calculation data model (usually referred to as a mesh) containing the coordinates (Vertex) of the vertices of each divided domain. Then, the solver process calculates the volume of the above-mentioned divided domain, the area of the boundary surface, and the normal vector of the boundary surface by using the Vertex and the like contained in the calculation data model, and then calculates physical values by using these values. The Vertex indicates values for setting forth the geometric shape of the divided domain. Thus, it is recognized that in a finite volume method, the solver process calculates the volume of the divided domain, the area of the boundary surface, and the normal vector of the boundary surface by using the geometric shape of the divided domain.
Further, in a finite volume method, a part may be provided where the vertex sharing condition for adjacent divided domains is not partly satisfied. Thus, in a finite volume method, restriction on the divided domain is somewhat alleviated in some cases. Nevertheless, the element type for analysis to be used is limited to, for example, a tetra element, a hexa element, a prism element, and a pyramid element.
Here, as shown in Patent Document 1, a finite volume method without limit of element type for analysis has also been proposed. Nevertheless, even in such a finite volume method without limit of element type for analysis, similarly to a conventional finite volume method described above, the pre process generates a calculation data model containing the coordinates (Vertex) of the vertices of each divided domain and then the solver process calculates physical values by using the Vertex contained in the calculation data model.
Further, as known widely, the finite element method is a method of calculating the physical values in each divided domain by using an interpolation function. However, similarly to a finite volume method, the solver process uses the geometric shape of the divided domain set forth by the Vertex and the like.
The voxel method and the particle method are methods for numerical analysis capable of easily generating a calculation data model in comparison with a finite element method and a finite volume method.
The voxel method is a method that voxel data for defining the analysis domain by using a plurality of voxels (an orthogonal grid) having a rectangular parallelepiped shape and basically the same size is generated as a calculation data model and that physical value calculation is performed by using the voxel data so that numerical analysis is achieved. Voxel methods are schematically divided into: a weighted residual type that uses a governing equation based on a weighted residual method; and a non-integration type that uses a cellular automaton model, a lattice Boltzmann model, or the like. Then, according to this voxel method, Vertex and the like to be used as voxel data are unnecessary.
According to such a voxel method, the analysis domain is easily defined by dividing the analysis domain into voxels. Thus, a calculation data model is generated in a short time.
On the other hand, the particle method is a method that particle data is generated as a calculation data model for defining the analysis domain by a plurality of particles and that physical value calculation is performed by using this particle data so that numerical analysis is achieved. The particle method of non-integration type uses an inter-particle interaction model as a governing equation. The particle method does not have divided domains, and hence does not require Vertex and the like. Thus, according to such a particle method, the analysis domain is easily defined by arranging particles uniformly in the analysis domain, so that a calculation data model is generated in a short time.